Phase matching of noncollinear sum and difference frequency high harmonic generation above and below the critical ionization level.

We investigate the macroscopic physics of noncollinear high harmonic generation (HHG) at high pressures. We make the first experimental demonstration of phase matching of noncollinear high-order-difference-frequency generation at ionization fractions above the critical ionization level, which normally sets an upper limit on the achievable cutoff photon energies. Additionally, we show that noncollinear high-order-sum-frequency generation requires much higher pressures for phase matching than single-beam HHG does, which mitigates the short interaction region in this geometry. We also dramatically increase the experimentally realized cutoff energy of noncollinear circularly polarized HHG, reaching photon energies of 90 eV. Finally, we achieve complete angular separation of high harmonic orders without the use of a spectrometer.